Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
141 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #64873 | C5 | direct (N × H) |
| 78. C52 | #332 | semidirect |
| 124. C5 | C5×#332 | semidirect |
| 125. C5 | #64873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4034 | 2 |
| C5×#4004 | 2 |
| #64873 | 5 |
| C5×#332 | 5 |